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Solve by Graphing

Perpendicular Lines and Points on the SAT: Desmos Walkthrough

You will find the equation, slope, or intercept of the line that is perpendicular to a given line and passes through a given point, then graph it in Desmos to confirm and read the answer.

This lesson solves by graphing: turn the equation into curves, then read intersections, vertices, or tangency straight off the Desmos graph.

Take this lesson interactively

A real SAT-style question

Line h is defined by 15x+17y-70=0. Line j is perpendicular to line h in the xy-plane. What is the slope of line j ?

A

-75

B

-57

C

75

D

57

How to solve it in Desmos, step by step

The idea

Graph line h, click its two gray axis-intercept dots to get two points on the line, then let Desmos compute line h's slope and the perpendicular slope as the negative reciprocal.

  1. 1

    Step 1

    Type this exactly as the equation of line h. Desmos draws the line right away.

    Type in Desmos

    15x+17y−70=0\frac{1}{5}x+\frac{1}{7}y-70=0
  2. 2

    Step 2

    Click the gray dot where line h crosses the x-axis. Desmos labels it as the point (350, 0).
  3. 3

    Step 3

    Click the gray dot where line h crosses the y-axis. Desmos labels it as the point (0, 490).
  4. 4

    Step 4

    Type this to let Desmos find the perpendicular slope. It is the negative reciprocal of the slope of line h, and Desmos shows 0.7142..., which equals 5 over 7. The answer is D.

    Type in Desmos

    m=490−00−350m=\frac{490-0}{0-350}s=−1ms=-\frac{1}{m}

The answer is D.

57

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

Line mm is defined by 14x+19y−50=0\frac{1}{4}x + \frac{1}{9}y - 50 = 0. Line nn is perpendicular to line mm in the xyxy-plane. What is the slope of line nn?

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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